Examine whether lim_"x→0"e^(1/x)/e^(1/x)+1 exits or not?
1 Answer
Feb 14, 2018
The limit does not exist.
Explanation:
Assume for the moment that x approaches 0 from the positive side.
Then we want
Let
The numerator and denominator approach infinity. Applying L'Hopital's Rule, take the derivatives of the numerator and denominator. Then the above equals:
Now assume that x approaches 0 from the negative side.
Then
The exponentials go to zero, and the denominator goes to 1.
Since the left- and right- and limits are not equal, the limit does not exist.